Answered: be a topology on Y. Let f be a mapping…

be a topology on Y. Let f be a mapping from X into Y defined by f(a)=f(b) = 3, f(c = 2 and f(d) = 1. Let g be mapping from X into Y defined by g(a) = 1, g(b)=g(c)=3 and g(d) = 2. Then %3D

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

alfa 0 O &
a |CI 3:03 PM
Let X = {a, b, c, d} and TX = {ø, X, {b},
{b,c}, {a,b,d}} be a topology on X. Let Y
= {1, 2, 3, 4} and TY = {Ø, Y, {3}, {1,2,3}}
be a topology on Y. Let f be a mapping
from X into Y defined by f(a)=f(b) = 3,
f(c) = 2 and f(d) = 1. Let g be mapping
from X into Y defined by g(a) = 1,
g(b)=g(c)=3 and g(d) = 2. Then
f is continuous and g is not
continuous
f is not continuous and g is
continuous
f and g are not continuous
f and g are both continuous
< O O
...

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